3.1 Dynamic characteristics of relative abundances and biodiversity of bacterial community in OE with and without LDXR
The relative abundances of Pseudomonas, Acinetobacter, Exiguobacterium, Sphingobacterium, Chryseobacterium, Arthrobacter, Brevundimonas, Microbacterium in OE with and without LDXR and corresponding Simpson diversity were obtained via periodical samplings and analyses, respectively (Fig. 1).
As illustrated in Figures 1, relative abundance of Pseudomonas, Acinetobacter, Exiguobacterium are significantly large than Sphingobacterium, Chryseobacterium, Arthrobacter, Brevundimonas, Microbacterium in OE without LDXR, which indicate many dominant species in bacterial community have been formed via CEP in OE without LDXR. However their relative abundances have a little difference in OE with LDXR, the individuals of different species appear uniform distribution without dominant species. The Simpson indexes of bacterial community demonstrate both the bacterial diversity in OE without LDXR was significantly large than with LDXR.
3.2. Hypothesis of formation and maintenance of bacterial diversity in OE without and with LDXR.
Based on microbial ecology, bioinformatics, cybernetics, observed phenomena, and experimental data (Fig.1), CA modeling and simulation for explanation of experimental phenomena and data were carried out according to following assumptions:
(1) The SII is related directly to the distance of bacterial individuals from substrate positions, the closer they are together, the stronger the SII. The bacterial individuals and descendants have capability of foraging for substrate by move and dispersal along the upgradient of SII to find the substrate positions.
(2) The bacterial individual could share substrate position information with other individuals within a certain distance, information sharing causes bacterial individuals to rapidly find the substrate position, increasing their survival probability. However the bacterial individual only shares substrate position information with other individuals who are close relatives in OE without LDXR. To the contrary, the bacterial individual shares substrate information with other individuals unconditionally regardless of kin relationship in OE with LDXR. This assumption is based on stress gradient hypothesis in ecology, that is different species tend to be more co-operative under abotic stress, while going to be more competitive in favorable environment (Lortie and Callaway 2006; Smit et al. 2009; Hammarlund and Harcombe 2019).
(3) As substrate position information is shared between bacterial individuals with close genetic relationship in OE without LDXR, they can quickly find the substrate position to become dominant species, while individuals of other species must spend longer foraging time and might die off due to starvation. Whereas individuals of different bacterial species can find the substrate position with the same possibility due to indiscriminated substrate position information sharing in OE with LDXR, hence dominant species can not easily be formed and protected a large number of species from extinction, greatly enhancing the evenness and richness of bacterial community to form and maintain bacterial diversity.
3.3. CA modeling and simulation for spatiotemporal succession of bacterial community in OE without and with LDXR
3.3.1 Cells
A cell with 6 states was defined as follows:
State space ={N(i, j), S(i, j), M(i, j), I(i, j), P(i, j), D(i, j)}
where (i, j) is the coordinate of grid on CS, both i and j are integers, and:
- N (i, j) denotes the number of by bacterial individuals colonizing on grid (i, j).
- S (i, j) denotes species of bacterial individuals colonizing on grid (i, j).
- M (i, j) denotes kinds of substrate on grid (i, j).
- I (i, j) denotes the SII at grid of (i, j).
- P (i, j) denotes whether or not a position (i, j) was occupied by bacterial individuals, and 1 and 0 represent “YES” and “NOT”, respectively.
- D (i, j) records the result of globally align nucleotide sequences of two bacterial individuals.
3.3.2 cellular space and Boundary Conditions
(1) Size of cellular space (CS): 2D domain with 103 × 103 square grids.
(2) Neighbor type: Moore-type neighbor type was applied for CA modeling and simulation, indicating each cell has 8 neighboring cells.
(3) Boundary conditions: periodic boundary signifying an infinite CS was applied for CA simulation to obtain a more general spatiotemporal succession pattern of bacterial community in OE with LDXR and without LDXR.
3.2.3. Update Rules
(1) Rule of substrate production
The substrates for bacterial growth and proliferation are come from air, the dust particles containing a small amount of macromolecular organic matters usually precipitate and scatter on the wall of X-ray inspection room. In order to simulate it, the different kinds of substrates were randomly computer-generated and placed in the CS with a period of ts.
(2) Rule of substrate information dissemination
According to hypothesis (1), the I(i, j) can be specified as follows:
where (i*, j*) is the coordinate of the substrate position, hence I(i*, j*) is the SII of the substrate position. In Eq. (1), if i = i*, j = j*, then I(i, j) = I(i*, j*).
(3) Rule of substrate consumption
If there are more than 100 bacterial individuals on the grid at (i*, j*), then S(i*, j*) = 0, indicating that substrate is run out.
(4) Information sharing and move rule.
This is key part of update rules of the CA modeling, because they sufficiently represent the two fundamentally different information sharing mechanisms driving spatiotemporal succession of bacterial community in OE without and with LDXR as follows:
For a single bacterial individual (mA) at the position of (i, j). If it does not get SII and there are no individuals within the scope of 3r, it will randomly move to its the nearest 8 neighboring grids with probability of pm until mA gets SII. Then mA randomly move to any one nearest neighboring grid whose SII is higher than the grid mA currently occupies with probability of ps, the above process is incrementally iterated until mA finds the substrate position.
However, if there is an another individual (mB) at the position of (i+x, j+y) within the scope of 3r, namely
the mA and mB might share information, otherwise they do not share information due to far distance. In OE without LDXR, whether or not mA and mB share information is dependent on the result of global alignment of their nucleotide sequences within the scope of 3r (Needleman and Wunsch 1970). If the calculated identity between the two sequences is not less than 70 %, mA and mB will share SII held by themselves each other, otherwise they will not do so (Fig.2).
In OE with LDXR, however, the bacterial individuals tend to be more cooperative against adversity stress, there the mA and mB will selflessly share SII held by themselves regardless of genetic relationship within the scope of 3r. Therefore, the proposed approach the mA and mB will find and reach substrate position is as follows:
The mA and mB respectively gets SII on the grid they currently occupy, then compare the SII of the 8 neighboring grids and randomly move to a grid whose SII is higher than grids currently occupied by themselves with probability of pmr, otherwise they will be in situ and do not move. The mA and mB will share SII with each other on the new grids they currently occupy, if the SII of the grid mA occupies is higher than the grid mB occupies, the mB will move or disperse step by step to the grid the mA currently occupies with probability of pc and uses this grid as its new starting point, and vice versa. The above process is incrementally iterated until both mA and mB finds the substrate position.
(5) Rule of birth and death. If a grid (i, j) is vacant, any one offspring of bacterial individuals on its neighboring grids within three layers (3r) can move to this position with the same probability pm. If a bacterial individual comes to death due to starvation with a probability pdh as it could not find the substrate position within specific foraging time limitation of tf. Based on the rule of Conway’s game of life, if a bacterial individual is surrounded with more than 3 nearest neighboring individuals, it would die with probability of pdc and gird it occupies is vacant due to intensified intra- and inter-specific competition. Furthermore, any individuals would die off naturally with same probability of pdn at each time step.
3.3 CA simulation
3.3.1 Spatial pattern of bacterial community succession in OE without and with LDXR
The S types of bacterial species with different individuals (S0) were also computer-generated to randomly and uniformly seed on the grids on CS. The M (M < S for simulating OE) kinds of substrate were randomly placed on Q positions (Q≤M) obeying two dimensional uniform distribution on CS through Monte Carlo experiments. Since a bacterial species could be considered as a nucleotide sequence, hence it could be generated by a random nucleotide sequence using finite alphabet method through Monte Carlo experiments and put to the CA model for simulation. In order to test the influence of different information sharing mechanisms on formation and maintenance of bacterial diversity in OE without and with LDXR, the different range of parameters were set in the model for Monte Carlo and CA simulation (Tab.2).
Table 2. Range of parameters in the CA model of bacterial community succession in OE both without LDXR and with LDXR
Name
|
Range of parameter
|
Unit
|
Significance
|
S
|
[5·102, 103]
|
dimensionless
|
Types of computer-generated bacterial species
|
S0
|
[10, 2·102]
|
dimensionless
|
Number of initial individuals of bacterial species
|
M
|
[2·102, 4·102]
|
dimensionless
|
Kinds of substrate were randomly placed on positions on the CS
|
Q
|
[102, 2·102]
|
dimensionless
|
Number of substrate positions randomly and uniformly generated on the CS.
|
ts
|
[1, 5]
|
day
|
Period of substrates randomly computer-generated and placed on the grids in the CS
|
pm
|
[0.4, 0.7]
|
dimensionless
|
Probability of a bacterial individual or its offspring moves or disperses to a vacant neighboring grid within three layers.
|
ps
|
[0.7, 1]
|
dimensionless
|
Probability of a bacterial individual or its offspring moving or dispersing to a neighboring grid whose SII is higher than it currently occupies.
|
pmr
|
[0.7, 1]
|
dimensionless
|
Probability of two individuals moving to neighboring grids with SII higher than grids currently occupied by themselves
|
pc
|
[0.8, 1]
|
dimensionless
|
Probability of an bacterial individual moving or dispersing to the grid another individual currently occupy through information sharing
|
pdh
|
[0.6, 0.9]
|
dimensionless
|
Probability of a bacterial individual coming to death due to starvation
|
tf
|
[4, 6]
|
day
|
Foraging time limitation a bacterial individual
|
pdc
|
[0.7, 1]
|
dimensionless
|
Probability of a bacterial individual coming to death due to intensified competition
|
pdn
|
[0.1, 0.4]
|
dimensionless
|
Probability of a bacterial individual coming to a natural death
|
I(i*, j*)
|
[50, 80]
|
dimensionless
|
SII of the substrate positions
|
Driven by different information sharing mechanisms of substrate position, the spatial pattern of bacterial community succession in OE without and with LDXR were emerged spontaneously and illustrated in Figure 3.
From Figure 3, differently spatial distribution patterns of bacterial individuals were emerged along with community succession. After the spatial patterns stabilization of bacterial community succession in OE without and with LDXR, the 10 different patches on CS were randomly and uniformly selected, and the phylogenetic analysis was conducted to investigate the similarity of bacterial individuals on these patches through calculation of the pairwise distances of nucleotide sequences and construction of a phylogenetic tree using the Jukes-Cantor distance method and the unweighted pair group method average (UPGMA) linkage method (Fig. 4), respectively (MathWorks 2021).
The Jukes-Cantor distance can measure the genetic relationship between bacterial individuals of different species. As illustrated in Figure 4, the bacterial individuals on selected patches are close affinities with smaller Jukes-Cantor distance as a result of selection mechanism through immediate relative information sharing in OE without LDXR. As a comparison, the bacterial individuals on selected patches that are not closely related due to larger Jukes-Cantor distance resulting from indiscriminated information sharing in OE with LDXR.
3.3.2 Temporal dynamic characteristics of bacterial community succession in OE without and with LDXR.
The temporal dynamic characteristics of bacterial community succession in OE without and with LDXR was obtained through accumulation of all individuals of the same species at different grids at the same time (Fig. 5), which is similar to double integral on 2D CS.
From Figure 5, the temporal dynamic response characteristics demonstrated that only a few bacterial species' population asymptotically stabilized via transient responses, while the most of species became minority species with small population or went distinct eventually in OE without LDXR. However, the bacterial community with higher evenness and more coexisting species whose number is far beyond given substrate types is ultimately formed and maintained in OE with LDXR, because the bacterial individuals of different species can exchange and share information of substrate positions unconditionally, the survival probabilities of all bacterial species’ individuals were increased, which can effectively prevent any bacterial species from being dominant and cause the bacterial community succession by a strategy of trading species for quantity.
The CA simulation results were highly similar to the phenomena and data observed in the experiments (Fig.1), and confirmed the hypothesis proposed, namely indiscriminated information sharing of substrate positions can greatly enhance the richenss and evenness of bacterial community and alleviate the intra- and inter-specific competition to form and maintain of the high bacterial diversity.
It is worth mentioning that the spatiotemporal succession patterns (Fig. 3 and 5) of bacterial community in OE without and with LDXR were quite general and universal, because these emerging spatiotemporal patterns were quite insensitive to initial values of state space, and parameters in the CA model.